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Regular Lévy Processes of Exponential type in 1D

In: Non-Gaussian Merton-Black-Scholes Theory

Author

Listed:
  • Svetlana I. Boyarchenko

    (University of Texas at Austin, USA)

  • Sergei Z. Levendorskiĭ

    (Rostov State University of Economics, Russia)

Abstract

AbstractThe following sections are included:Model ClassesAn overviewKoBoL family: direct construction via the Lévy-Khintchine formulaDefinition in terms of the Lévy measureThe characteristic exponentMoments of a KoBoL processGraphs of characteristic exponents and probability densities of different KoBoL processesProofs of technical lemmasNormal Inverse Gaussian processes and Normal Tempered Stable Lévy Processes: construction via subordinationVariance Gamma ProcessesHyperbolic Processes and Generalized Hyperbolic ProcessesComparison of the tail behaviour of probability densities for different model classes of processesTwo definitions of Regular Lévy Processes of Exponential typeDefinition in terms of the Lévy measureDefinition in terms of the characteristic exponentProperties of the characteristic exponents and probability densities of RLPEProperties of the infinitesimal generatorsA “naive approach” to the construction of RLPE or why they are natural from the point of view of the theory of PDOModified Stable Processes and RLPEThe Wiener-Hopf factorizationThe case of Lévy processes of exponential typeThe Wiener-Hopf factorization for RLPEApproximate formulas for the factors in the case of NIG, HP, KoBoL and NTS Lévy processes

Suggested Citation

  • Svetlana I. Boyarchenko & Sergei Z. Levendorskiĭ, 2002. "Regular Lévy Processes of Exponential type in 1D," World Scientific Book Chapters,in: Non-Gaussian Merton-Black-Scholes Theory, chapter 3, pages 67-96 World Scientific Publishing Co. Pte. Ltd..
  • Handle: RePEc:wsi:wschap:9789812777485_0003
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    Keywords

    Non-Gaussian Models; Merton-Black-Scholes Theory; Levy Processes; American Options; European Options; Feller Processes;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • A1 - General Economics and Teaching - - General Economics
    • A2 - General Economics and Teaching - - Economic Education and Teaching of Economics
    • E6 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook

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